The Binomial Expansion

We can use the binomial theorem to expand and simplify expressions of the formwhere n is any positive whole number.

The general expansions is

Example:

We evaluate the coefficient of each power ofand simplify:

Example:

which simplifies to

then

Suppose we have an expansion. We knowand but not n. If we have a relationship between the coefficients we may be able to form an equation to find n. Suppose in the expansion below we know that the coefficient ofequals the coefficient of